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But the group theory is in the algebra is most ancient one of richest branches, is the modern algebra foundation.

而群论是代数学中最古老最丰富的分支之一，是近世代数的基础。

Develop the formulation of the the Lie group, Lie algebra and Riemannian manifolds and spatial operator algebra.

建立了Lie群和Lie代数、Riemannian流形与空间算子代数理论联系的模型。

This article continues to study the application of rough set theory rough and algebra system -group, rings to combine research. So that rough algebra system is built better perfectly.

本文继续将粗糙集理论与代数系统——群、环理论结合起来进行研究，以此建立比较完善的粗糙代(来源：0cbdAcbBC论文网www.abclunwen.com)数系统。

One points at a sequence of one sparse linear algebra system of equation ,utilizing frequent treatment sparse matrix data structure at present that is according to the competent store structure, design the law of conjugation gradient method which solves the equation group of the sparse linear algebra of asking analyses the complexity of calculating.

第一部分针对一类稀疏线性代数方程组，利用目前国际上使用比较频繁的处理稀疏矩阵的按行稀疏存储结构，设计了求解稀疏线性代数方程组的共轭梯度法，并分析计算复杂度。

In chapter 2, we study a kind of operator algebra acted on the Hilbert space H which is called the closed weakly reducible maximal triangular algebra, denoted by S.

第二章我们研究了一个作用在Hilbert空间Η上的闭弱可约极大三角代数S，证明了S的系数在Β中的任意阶完全有界Hochschild上同调群H_~nS，Β(Η(n≥1)是平凡的。

He has been working on the teaching of Higher Mathematics, Linear Algebra, Probability Statistics, Higher Algebra, Matrix Theory, Mathematical Statistics, and Stochastic Process, etc.

从事高等数学、线性代数、概率统计、高等代数、矩阵理论、数理统计、随机过程等课程。

Notable examples are the development of category theory, which provides a useful framework for a large part of mathematics, homological algebra, and applications of model theory to algebra.

比较明显的例子是范畴论的发展，范畴论对数学，同调代数，以及模论在代数上的应用都提供了一个十分有用的框架。

In [3], Beligiannis developed a homological algebra in C which parallels the homological algebra in an exact category in the sense of Quillen.

在文[3]中，Beligiannis沿此思路研究了三角范畴的同调性质。

In the chapter two, we will recall some basic concepts and propertiesin commutative algebra and homological algebra. In the chapter three,wewill defineⅠ-flat modules and give equivalent conditions: one module M isanⅠ-flat R-module if and only if for all prime ideals p,SuppTor_1~R

本文首先介绍了关于平坦模的一些基本概念和性质，而后将平坦模的概念在一定意义上进行推广，定义了I-平坦模，并得到了模M是I-平坦R-模的等价条件：对R中所有素理想p，有suppTor_1~R

It takes advantages of AR-quiver analysis and APR- tilting translation. We proved: if T_A is a tilting A-module over a path algebra of type A_n or a characteristic tilting A-module over a path algebra of type D_n,E_6,E_7, E_8,then there are points corresponding indecomposable direct summands of T_A in theτ- orbit of each edge.

通过对Dynkin型路代数的AR-箭图分析及利用APR-倾斜变换，证明了A_n型路代数倾斜模及D_n，E_6，E_7，E_8型路代数本性倾斜模T_A的一个必要条件是，在A的AR-箭图Γ_A的边缘的r-轨道都有T_A的不可分解直和项对应的点。

This paper designs the communication system of radio telescope FAST.

针对500m口径球面射电望远镜FAST分布式控制系统的特点完成了其通信系统的设计。

Political sheep's step-by-step a large number of fossils unearthed in the county soil Ma Ali after rural village in the middle of sallow pelitic siltstone.

步氏和政羊化石大量出土于广河县阿力麻土乡后山村，产于灰黄色泥质粉砂岩中。